This paper presents the results of molecular dynamic modeling, revealing that inserting confined graphene layers into copper crystal reduces the thermal conductivity of the whole composite, and the coefficient of thermal conductivity κ decreases upon an increase in the number of graphene layers. The injection of one, two, and three layers of 15 nm graphene leads to a change in the coefficient of thermal conductivity from 380 W/(m·K) down to 205.9, 179.1, and 163.6 W/(m·K), respectively. Decreasing the length of graphene layers leads to a decrease in the density of defects on which heat is dissipated. With one, two, and three layers of 8 nm graphene, the coefficient of thermal conductivity of the composite is equal to 272.6, 246.8, and 240.8 W/(m·K), appropriately. Meanwhile the introduction of an infinite graphene layer results in the growth of κ to 414.2–803.3 W/(m·K).